Least Common Multiple (LCM) of 68 and 39
The least common multiple (LCM) of 68 and 39 is 2652.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 68 and 39?
First, calculate the GCD of 68 and 39 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 39 = 1 remainder 29 |
| 2 | 39 ÷ 29 = 1 remainder 10 |
| 3 | 29 ÷ 10 = 2 remainder 9 |
| 4 | 10 ÷ 9 = 1 remainder 1 |
| 5 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 58 | 10150 |
| 55 and 161 | 8855 |
| 110 and 35 | 770 |
| 152 and 105 | 15960 |
| 95 and 42 | 3990 |